Multi-point Codes over Kummer Extensions

Abstract

This paper is concerned with the construction of algebraic geometric codes defined from Kummer extensions. It plays a significant role in the study of such codes to describe bases for the Riemann-Roch spaces associated with totally ramified places. Along this line, we give an explicit characterization of Weierstrass semigroups and pure gaps. Additionally, we determine the floor of a certain type of divisor introduced by Maharaj, Matthews and Pirsic. Finally, we apply these results to find multi-point codes with good parameters. As one of the examples, a presented code with parameters $[254,228,⩾16]$ over ${\mathbb{F}}_{64}$ yields a new record.

15 pages

References in corpus (2)

• One- and Two-Point Codes over Kummer Extensions
• Algebraic Geometric codes from Kummer Extensions

Cited by in corpus (7)

• Weierstrass Semigroups from Kummer Extensions
• Pure gaps on curves with many rational places
• Weierstrass Semigroup, Pure Gaps and Codes on Function Fields
• Multi-point Codes from the GGS Curves
• Weierstrass Pure Gaps From a Quotient of the Hermitian Curve
• Weierstrass Semigroups From a Tower of Function Fields Attaining the Drinfeld-Vladut Bound
• Explicit bases for Riemann-Roch spaces on elliptic curves and their application in constructing various elliptic code families